# How do I find the derivative of #f(x)=ln(abs(x))#?

##### 1 Answer

Jan 4, 2016

#### Explanation:

This can be split into a piecewise function.

#f(x)={(ln(x)",","if "x>0),(ln(-x)",","if "x<0):}#

Find the derivative of each part:

#d/dx(ln(x))=1/x#

#d/dx(ln(-x))=1/(-x)*d/dx(-x)=1/x#

Hence,

#f'(x)={(1/x",","if "x>0),(1/x",","if "x<0):}#

This can be simplified, since they're both

#f'(x)=1/x#

Even though